Abstract: When utilizing the location based service along the movement, the reported location of users will emerge a gradual ascending of sensitivity by characteristics of moving to the target. With the trend of sensitivity ascending, the adversary can identify the destination of a particular and even some other privacy information that jeopardize the security of the user. In order to cope with this type of attack and from acquiring, this paper proposes an ε-sensitive indistinguishable algorithm based on the conception of generalized differential privacy and Voronoi diagram. In this algorithm, the current region is divided by Voronoi diagram to calculate the value of location sensitivity then grids of diagram sensitivity that the contour will be generated, so dummies are added to current grids to achieve ε-sensitive indistinguishable for users in each grid. As a result, the gradually ascending sensitivity value of any particular user will be difficult to identify, and the privacy can be protected. However, the results of simulation experiment deployed in both of Euclidean space and road network showed that, plenty of dummy locations would affect the quality of location service in both of execution and calculation times, so an improvement with location shift version of this algorithm is proposed. At last, through the security analysis for the model of ε-sensitive indistinguishable as well as the experimental verification for two versions of this algorithm, this algorithm is better to be deployed in real environment and has a better level of location privacy than other similar algorithms. Accordingly, this algorithm can prevent the user from attacks of the adversary utilizing the trend of sensitivity ascending and protect the privacy of the user during the continuous movement.